Question

A car slams on its brakes, coming to a complete stop in 4.0 s. The car was traveling south at 60.0 mph. Calculate the acceleration.

Answer 1

Acceleration,
`a=-6.705\ m/s^2`

Step-by-step explanation:

It is given that,

Final velocity of the car, v = 0

Initial velocity of the car, u = 60 mph = 26.82 m/s

It comes to rest in 4 s

We need to find its acceleration. The rate of change of velocity is called its acceleration. Mathematically, it is given by :

`a=(v-u)/(t)`

`a=(0-26.82\ m/s)/(4\ s)`

`a=-6.705\ m/s^2`

So, the car is decelerating with a magnitude of 6.705 m/s^2. hence, this is the required solution.

Answer 2

`\vec{a}=(5.45*10^4(mi)/(h^2))\hat{j}`

Step-by-step explanation:

Using the y-axis as a reference system, for which the north is positive and the south is negative, we have:

`\vec{v_0}=(-60mph)\hat{j}`

The acceleration is given by this kinematic equation:

`\vec{a}=\frac{\vec{v_f}-\vec{v_0}}{t}`

We do the conversion from seconds to hours:

`4s*(1h)/(3600s)=1.1*10^(-3)h`

Finally, replacing the given values:

`\vec{a}=\frac{0-(-60mph)\hat{j}}{1.1*10^(-3)h}\\\vec{a}=(5.45*10^4(mi)/(h^2))\hat{j}\\`