Car is driving with a speed of 36km/h. Then the car stops completely in 2 seconds. What is the negative acceleration of the car?

I know that this is a very easy problem but I'd be very happy if someone could write the steps of it. Thank you

Aug 16, 2017

${a}_{x} = - 6.48 \times {10}^{4}$ ${\text{km/h}}^{2}$ $= - 5.00$ ${\text{m/s}}^{2}$

Explanation:

We're asked to find the acceleration of the car, given its initial speed and how long it takes to stop.

To do this, we can use the equation

${v}_{x} = {v}_{0 x} + {a}_{x} t$

where

• ${v}_{x}$ is the final velocity of the car

• ${v}_{0 x}$ is the initial velocity of the car

• ${a}_{x}$ is the constant acceleration of the car (what we're trying to find)

• $t$ is the time

We know:

• ${v}_{0 x} = 36 \textcolor{w h i t e}{l} \text{km/h}$

• $t = 2$ $\text{s}$ = ul(5.56 xx 10^-4color(white)(l)"h" (units must be consistent)

• and the final velocity ${v}_{x} = 0$, because it comes to a stop

Plugging i known values:

0 = 36color(white)(l)"km/h" + a_x(5.56xx10^-4color(white)(l)"h")

color(red)(ulbar(|stackrel(" ")(" "a_x = -6.48xx10^4color(white)(l)"km/h"^2 = -5.00color(white)(l)"m/s"^2" ")|)

The acceleration of the car is thus color(red)(-6.48xx10^-4color(white)(l)"kilometers per hour per hour", which is equal to color(red)(-5.00color(white)(l)"meters per second per second".