# A car accelerates from 32.0m/s to rest with an acceleration of -3.20m/s^2. What is the car's displacement from t=2 to t=3 seconds? What is the car's displacement from t=4 to t=5 seconds?

Oct 30, 2017

A)24m
B)17.6m

#### Explanation:

1. From $t = 2$ to $t = 3$ ,

First, we'll find the velocity at time 2s.

$v = u + a t$
$= 32 \frac{m}{s} + \left(- 3.2\right) \frac{m}{s} ^ 2 \cdot 2 s$
$= 25.6 \frac{m}{s}$

Now, we'll substitute that in the displacement equation, with time being 1s (the time between $t = 2$ to $t = 3$)

$S = u t + 0.5 a {t}^{2}$
$= 25.6 \frac{m}{\cancel{s}} \cdot 1 \cancel{s} + 0.5 \cdot \left(- 3.2\right) \frac{m}{\cancel{s}} ^ 2 \cdot {\left(1 \cancel{s}\right)}^{2}$
$= 24 m$

$- - - - - - - - - -$

2. From $t = 4$ to $t = 5$ ,

$v = u + a t \to \text{ speed at } 4 s$
$= 32 + \left(- 3.2\right) 4$
$= 19.2 \frac{m}{s}$
$S = u t + 0.5 a {t}^{2}$
$= 19.2 \cdot 1 + 0.5 \cdot \left(- 3.2\right) \cdot {1}^{2}$
$= 17.6 m$