Q: Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of 60 km / h in the direction X to Y notices that a

t _1=30 ~min = 1 2 hr aligned t _2 & =10 ~min = 1 6 hr \\ ~V _ B & = Speed of Bus \\ V _ S & = Speed of scooty (girl) aligned (Same direction) (Opposite direction) aligned & d= (V_B-V_S ) t_1= (V_B+V_S ) t_2 \\ & (V_B-60 ) 1 2 = (V_B+60 ) 1 6 \\ & 3 V_B-180=V_B+ 60 \\ & 2 V_B=240 \\ & V_B=120 ~km / hr aligned Distance = ( V _ B - V _ S ) t _1 aligned & D =(120-60) 1 2 =30 ~km \\ & t = d ~V _ B = 30 120 = 1 4 hr =15 ~min aligned

Q: In some appropriate units, time (t) and position ( x ) relation of a moving particle is given by t=x^2+x. The acceleration of the particle is

aligned & t=x^2+x \\ & dt dx = d dx [ x ^2+ x ] \\ & 1 v =2 x +1 aligned v=(2 x+1)^ -1 ...(i) aligned a & = v d v d x =(2 x+1)^ -1 [-1(2 x+1)^ -2 2 ] \\ a & =-1(2 x+1)^ -3 2 \\ a & =-2(2 x+1)^ -3 \\ & =- 2 (2 x+1)^3 aligned

Q: Two heaters A and B have power rating of 1 kW and 2 kW , respectively. Those two are first connected in series and then in parallel to a fixed power source. The ratio of power outputs for these two ca

aligned & Power Consumed =P= V^2 R \\ & P_A P_B = R_B R_A \\ & R_A=2 R_B aligned For Series Combination P_S= V^2 3 R_B For Parallel Combination aligned & P_P= 3 V^2 2 R_B \\ & P_S P_P = 2 9 aligned

Question 1

The following plots show variation of velocity (v) with time (t), of a ball thrown vertically upward, and falling back. Which of the following plots is/are correct ?

Accepted Answer

Let the upward direction be considered positive. When a ball is thrown vertically upward with an initial velocity u, it moves under the constant downward acceleration due to gravity (a = -g). The velocity v at any time t is given by the kinematic equation: v = u + at v = u - gt This equation represents a straight line with a positive y-intercept (u) and a constant negative slope (-g). Initially, the velocity is positive and decreases linearly until it becomes zero at the highest point. As the ba

Question 2

Consider a particle moving along a straight line, whose position as a function of time is given by s(t)= t^2- t+ , where =1 ms^ -2 , =6 ms^ -1 and =5 m. The average speed of the particle, in ms^ -1 ,

Accepted Answer

Given s(t) = t^2 - 6t + 5 Velocity v(t) = ds dt = 2t - 6 The particle comes to rest when v(t) = 0, which gives t = 3 s. Position at t = 0 s is s(0) = 5 m. Position at t = 3 s is s(3) = 3^2 - 6(3) + 5 = -4 m. Position at t = 6 s is s(6) = 6^2 - 6(6) + 5 = 5 m. Distance travelled from t = 0 to t = 3 s is d_1 = |-4 - 5| = 9 m. Distance travelled from t = 3 to t = 6 s is d_2 = |5 - (-4)| = 9 m. Total distance travelled is D = d_1 + d_2 = 9 + 9 = 18 m. Average speed = 18 6 = 3 ms^ -1 Answer: 3

Question 3

When a ruler falls vertically, 5 different persons catch it with different reaction times. (g = 9.8 m s^ -2 ) A. Person A has reaction time of 0.20 s. B. Person B has reaction time of 0.22 s. C. Perso

Accepted Answer

The distance travelled by the ruler falling freely under gravity is given by d = 1 2 g t^2. Since g is constant, the distance d is directly proportional to the square of the reaction time t. Thus, a larger reaction time results in a greater distance travelled by the ruler. The given reaction times are: t_A = 0.20 s t_B = 0.22 s t_C = 0.18 s t_D = 0.19 s t_E = 0.21 s Arranging the reaction times in descending order: 0.22 > 0.21 > 0.20 > 0.19 > 0.18 This corresponds to: t_B > t_E > t_A > t_D > t_C

Question 4

Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of 60 km / h in the direction X to Y notices that a

Accepted Answer

t _1=30 ~min = 1 2 hr aligned t _2 & =10 ~min = 1 6 hr \ ~V _ B & = Speed of Bus \ V _ S & = Speed of scooty (girl) aligned (Same direction) (Opposite direction) aligned & d= (V_B-V_S ) t_1= (V_B+V_S ) t_2 \ & (V_B-60 ) 1 2 = (V_B+60 ) 1 6 \ & 3 V_B-180=V_B+ 60 \ & 2 V_B=240 \ & V_B=120 ~km / hr aligned Distance = ( V _ B - V _ S ) t _1 aligned & D =(120-60) 1 2 =30 ~km \ & t = d ~V _ B = 30 120 = 1 4 hr =15 ~min aligned

Question 5

In some appropriate units, time (t) and position ( x ) relation of a moving particle is given by t=x^2+x. The acceleration of the particle is

Accepted Answer

aligned & t=x^2+x \ & dt dx = d dx [ x ^2+ x ] \ & 1 v =2 x +1 aligned v=(2 x+1)^ -1 ...(i) aligned a & = v d v d x =(2 x+1)^ -1 [-1(2 x+1)^ -2 2 ] \ a & =-1(2 x+1)^ -3 2 \ a & =-2(2 x+1)^ -3 \ & =- 2 (2 x+1)^3 aligned

Question 6

Two heaters A and B have power rating of 1 kW and 2 kW , respectively. Those two are first connected in series and then in parallel to a fixed power source. The ratio of power outputs for these two ca

Accepted Answer

aligned & Power Consumed =P= V^2 R \ & P_A P_B = R_B R_A \ & R_A=2 R_B aligned For Series Combination P_S= V^2 3 R_B For Parallel Combination aligned & P_P= 3 V^2 2 R_B \ & P_S P_P = 2 9 aligned

Question 7

A particle is moving along x-axis with its position (x) varying with time (t) as x= t^4+ t^2+ t+ . The ratio of its initial velocity to its initial acceleration, respectively, is:

Accepted Answer

Position of particle, x= t^4+ t^2+ t+ Velocity v= d x d t =4 t^3+2 t+ Initial velocity =v(t=0)= Acceleration a= d v d t =12 t^2+2 Initial acceleration =a(t=0)=2 v(t=0) a(t=0) = 2

Question 8

The velocity (v) - time (t) plot of the motion of a body is shown below: The acceleration (a) - time (t) graph that best suits this motion is :

Accepted Answer

Initially, the body has zero velocity and zero slope. Hence the acceleration would be zero initially. After that, the slope of v-t curve is constant and positive. After some time, velocity becomes constant and acceleration is zero. After that, the slope of v-t curve is constant and negative.

Motion In One Dimension — Previous Year Questions & Solutions