Question

A car braked with a constant deceleration of 64 ft/s2, producing skid marks measuring 50 ft before coming to a stop. How fast was the car traveling when the brakes were first applied?

Answer 1

Answer:

The inicial speed of the car was 80 feet per hour.

Step-by-step explanation:

To solve this problem, we can use Torricelli formula to calculate the inicial speed of the car:

V2 = Vo2 + 2*a*D

where V is the final speed, Vo is the inicial speed, a is the acceleration and D is the total distance travelled.

Using V=0, a=-64 and D=50, we have:

0 = Vo2 + 2*(-64)*50

Vo2 = 2*64*50 = 6400

Vo = 80 ft/s

The inicial speed of the car was 80 feet per hour.

Answer 2

Answer:

The initial speed of the car was 80 ft/s.

Step-by-step explanation:

The deceleration is the rate at which the car speed decreases. In this case the speed of the car goes all the way down to 0 ft/s and in order to do that it travelled 50 ft.  So we will call the initial speed at which the car started to brake "v_0" and use Torricelli's equation to find it. The equation is given by:

v^2 = (v_0)^2 + 2*a*S

Where v is the final speed, v_0 is the initial speed, a is the rate of acceleration and S is the space travelled. Using the values that the problem gave to us we have:

0^2 = (v_0)^2 - 2*64*50

0 = (v_0)^2 - 6400

(v_0)^2 = 6400

v_0 = sqrt(6400) = 80 ft/s

Notice that in this case "a" was negative, since the car was decelerating instead of accelerating.

The initial speed of the car was 80 ft/s.