A particle travels in a circle of radius 1.0 cm with a speed given by v = 2.0 t , where v is in cm/s and t is in seconds. Calculate the magnitude of the particle's acceleration at t = 1 s .

Step-by-step solution

The speed of the particle is given by v = 2.0 t . The tangential acceleration is the rate of change of speed: a_t = dv dt = 2.0 cm/s ^2 At t = 1 s , the speed is: v = 2.0(1) = 2.0 cm/s The radial (centripetal) acceleration is: a_r = v^2 R = (2.0)^2 1.0 = 4.0 cm/s ^2 The total acceleration is the vector sum of the tangential and radial accelerations: a = a_t^2 + a_r^2 a = (2.0)^2 + (4.0)^2 a = 4.0 + 16.0 = 20 cm/s ^2