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

1 Answer
Aug 16, 2017

a_x = -6.48xx10^4ax=6.48×104 "km/h"^2km/h2 = -5.00=5.00 "m/s"^2m/s2

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_(0x) + a_xtvx=v0x+axt

where

  • v_xvx is the final velocity of the car

  • v_(0x)v0x is the initial velocity of the car

  • a_xax is the constant acceleration of the car (what we're trying to find)

  • tt is the time

We know:

  • v_(0x) = 36color(white)(l)"km/h"v0x=36lkm/h

  • t = 2t=2 "s"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".