Question

A truck on a straight road starts from rest, accelerating at 2.00 m/s2 until it reaches a speed of 20.0 m/s. Then the truck travels for 20 s at a constant speed until the brakes are applied, stopping the truck in a uniform manner in an additional 5.00 s. (a) How long is the truck in motion? (b) What is the average velocity of the truck for the motion described?

Answer 1

Let's determine the travel time and distance for each section of the path

1) For the first leg of the path

$t_1=\frac{v}{a_1}=\frac{20}{2}=10s$

$s_1=\frac{a\cdot {t_1}^2}{2}=\frac{2\cdot 10^2}{2}=100m$

2)For the second leg

$t_2=20s$

$s_2=v \cdot t_2=20 \cdot 20=400m$

3)For the third leg

$t_3=5s$

Determine the acceleration with which the truck slows down

$a_3=\frac{v}{t_3}=\frac{20}{5}=4m/s^2$

then

$s_3=v \cdot t_3-\frac{a_3\cdot {t_3}^2}{2}=20 \cdot 5-\frac{4\cdot 5^2}{2}=50m$

a)the truck is in motion

$t=t_1+t_2+t_3=10+20+5=35s$

b)average speed of the truck during the described movement

$v_m= \frac{s_1+s_2+s_3}{t_1+t_2+t_3}=\frac{100+400+50}{10+20+5}=15.714m/s$