Question

a car and a truck start from rest at the same instant, with the car initially at some distance behind the truck. the truck has a constant acceleration of 2.10 m/s² and the car an acceleration of 3.40 m/s². the automobile overtakes the truck after the truck has moved 60.0 m. part c: what is the speed of the truck when they are abreast? express your answer with the appropriate units.

Explanation:

Step1: Find time when car overtakes truck

First, we know the truck's displacement \( s_{truck} = 60.0\space m \) and its acceleration \( a_{truck}=2.10\space m/s^2 \). The truck starts from rest, so initial velocity \( u_{truck} = 0 \). Using the equation of motion \( s = ut+\frac{1}{2}at^2 \) for the truck:
\( 60.0 = 0\times t+\frac{1}{2}\times2.10\times t^2 \)
\( 60.0 = 1.05t^2 \)
Solving for \( t \):
\( t^2=\frac{60.0}{1.05} \)
\( t^2\approx57.14 \)
\( t = \sqrt{57.14}\approx7.56\space s \)

Step2: Calculate truck's speed at that time

Using the equation \( v = u+at \) for the truck ( \( u = 0 \), \( a = 2.10\space m/s^2 \), \( t\approx7.56\space s \)):
\( v_{truck}=0 + 2.10\times7.56 \)
\( v_{truck}\approx15.88\space m/s \)

Answer:

The speed of the truck when they are abreast is approximately \( \boldsymbol{15.9\space m/s} \) (or more precisely \( 15.88\space m/s \)).