Question

1. a car accelerates from rest at a rate of 5.00 m/s² for 4.00 seconds. the car then travels at a constant velocity for 15.0 seconds. calculate the total displacement of the car.

Explanation:

Step1: Calculate the velocity after acceleration

Use the formula $v = v_0+at$. Here, $v_0 = 0$ (starts from rest), $a = 5.00\ m/s^2$, and $t = 4.00\ s$.
$v=0 + 5.00\times4.00=20.0\ m/s$

Step2: Calculate the displacement during acceleration

Use the formula $x_1=v_0t+\frac{1}{2}at^{2}$. Since $v_0 = 0$, $a = 5.00\ m/s^2$, and $t = 4.00\ s$.
$x_1=0\times4.00+\frac{1}{2}\times5.00\times4.00^{2}=\frac{1}{2}\times5.00\times16 = 40.0\ m$

Step3: Calculate the displacement during constant - velocity motion

The car moves at a constant velocity $v = 20.0\ m/s$ for $t_2=15.0\ s$. Use the formula $x_2=v\times t_2$.
$x_2=20.0\times15.0 = 300\ m$

Step4: Calculate the total displacement

The total displacement $x=x_1 + x_2$.
$x=40.0+300=340\ m$

Answer:

$340\ m$