Question

"A car is travelling at 70 m/s. The driver sees a cow in the road and slows down with a constant acceleration for 10 seconds before coming to a stop. What is the car’s displacement by the time is stops." what information do you know?

Answer 1

The question does not ask for anything in particular. I will calculate the acceleration and distance.

Answer:

The acceleration of the car is
`-7\ m/s^2`

The distance traveled before stopping is 350 m

Step-by-step explanation:

Constant Acceleration Motion

It's a type of motion in which the velocity of an object changes by an equal amount in every equal period of time.

Being a the constant acceleration, vo the initial speed, vf the final speed, and t the time, the following relation applies:

`v_f=v_o+at\qquad [1]`

The distance traveled by the object is given by:

`\displaystyle x=v_o.t+(a.t^2)/(2)\qquad [2]`

The car has an initial speed of v0=70 m/s when the driver sees a cow in the road and steps on the brakes with an (assumed) constant acceleration during t=10 seconds before stopping (vf=0).

With the information provided, we can calculate the value of the acceleration and the distance traveled.

Using the equation [1] we can solve for a:

`\displaystyle a=(v_f-v_o)/(t)`

Substituting the numerical values:

`\displaystyle a=(0-70)/(10)=-7\ m/s^2`

The acceleration of the car is
`-7\ m/s^2`

The distance is now calculated by using [2]

`\displaystyle x=70\cdot 10+((-7)\cdot 10^2)/(2)`

`\displaystyle x=700-(700)/(2)=350\ m`

The distance traveled before stopping is 350 m