Question

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

Answer 1

`a_x = -6.48xx10^4` `"km/h"^2` `= -5.00` `"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_(0x) + a_xt`

where

• `v_x` is the final velocity of the car

• `v_(0x)` 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_(0x) = 36color(white)(l)"km/h"`

• `t = 2` `"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"`.