Question

A car starts from rest and accelerates at a constant rate travelling a distance of 160 m in 6 s. The car continues to accelerate at the same rate for an additional x m. If the speed of the car after it has travelled the (160+ x) m is 92 m/s, how far x (in m) did the car continue at a constant acceleration?

Answer 1

First determine the magnitude of acceleration of the car.

Suppose, acceleration of the car = a

distance traveled, s = 160 m

Time taken to cover this distance, t = 6 s

use the formula -

s = u*t + (1/2)*a*t^2

=> 160 = 0 + 0.5*a*6^2 [initial speed of the car, u = 0]

=> a = 160 / (0.5*6^2) = 8.9 m/s^2

Now, final speed of the car, v = 92 m/s

find out the time for achieving this speed.

v = u + a*T

=> 92 = 0 + 8.9*T

=> T = 92 / 8.9 = 10.3 s

So, distance traveled in this time T -

s' = u*T + (1/2)*a*T^2

= 0 + 0.5*8.9*10.3^2 = 475.5 m

Means,

160 + x = 475.5

=> x = 475.5 - 160 = 315.5 m (Answer)