A car moving at a speed v is stopped by a retarding force F in a distance s . If the retarding force were 3 F , then the car will be stopped in a distance

Step-by-step solution

Given that, initial speed of car, v_i=v Final speed of car when it stops, v_f=0 Distance travelled =s Retarding force =F By Newton's law of motion, aligned F=m a & =m ( v_f^2-v_i^2 2 s ) (i) [ array l using relation a= v_f^2-v_i^2 2 s array ] & = m (-v^2 ) 2 s F & = -m v^2 2 s aligned When, retarding force, F^ =3 F Let s^ = New distance travelled. Similarly, from Eq. (i) we can write 3 F= -m v^2 2 s^ ...(ii) Substituting value of F from Eq. (i) into Eq. (ii), we get 3 ( -m v^2 2 s )= -m v^2 2 s^ s^ =s / 3 Hence, th