Question

A truck covers 32.0 m in 8.70 s while smoothly slowing down to final speed of 2.10 m/s. (a) Find its original speed. Incorrect: Your answer is incorrect. Does it make sense in this problem that the initial velocity is smaller than the final velocity? m/s (b) Find its acceleration. (Indicate the direction of the acceleration with the sign of your answer.)

Answer 1

Explanation:

Given that,

Distance covered, d = 32 m

Time, t = 8.7 m

Final speed of the truck, v = 2.1 m/s

(a) Let a is the acceleration and u is the original speed of the truck.

Using first equation of kinematics as :

$v=u+at$

$2.1=u+8.7a$..............(1)

Using second equation of kinematics as :

$d=ut+\dfrac{1}{2}at^2$

$32=u(8.7)+\dfrac{1}{2}a(8.7)^2$...........(2)

On solving equation (1) and (2) we get :

Original speed, $u=5.25\ m/s$

(b) Acceleration, $a=-0.36\ m/s^2$

Hence, this is the required solution.