A car traveling 56 km/h is 21.0 m from a barrier when the driver slams on the brakes. The car hits the barrier 2.17 s later.

a)What was the car's constant deceleration before impact?

b)How fast was the car traveling at impact?

First you must change 56 km/h to m/s. In m/s the Initial Velocity is 15.56 m/s. Next use the equation:

S = ViT + (1/2)at^2 and solve for a

21 = (15.56)(2.17) + (1/2)(a)(2.17)^2

a = -5.42 m/s^2

Now that you have the acceleration you can solve for the final velocity using either:

Vf = Vi + at ---or--- Vf^2 = Vi^2 + 2as

Vf = 15.56 + (-5.42)(2.17) = 3.8 m/s
or
Vf^2 = 15.56^2 + 2(-5.42)(21) = 3.8 m/s

As you can see each equation gave the same answer. Overall your answers would be:

a.) -5.42 m/s^2
b.) 3.8 m/s

thanks

To answer these questions, we can use the equations of motion, specifically the equation that relates displacement, initial velocity, time, and acceleration:

displacement = initial velocity * time + (1/2) * acceleration * time^2

Let's break down the problem step by step:

a) What was the car's constant deceleration before impact?

We are given the following information:
- Initial velocity (u) = 56 km/h
- Displacement (s) = 21.0 m
- Time (t) = 2.17 s

First, we need to convert the initial velocity from km/h to m/s, as we are using SI units in this equation.

1 km = 1000 m and 1 hour = 3600 seconds, so:
Initial velocity (u) = 56 km/h = 56 * (1000 m/3600 s) = 15.56 m/s

Now let's solve for the deceleration (a) using the equation of motion. Rearranging the equation, we have:
displacement = initial velocity * time + (1/2) * acceleration * time^2

Plugging in the known values:
21.0 m = (15.56 m/s) * (2.17 s) + (1/2) * acceleration * (2.17 s)^2

Simplify the equation:
21.0 m = 33.75 m + 1.087 * acceleration

Rearranging the equation to solve for acceleration:
Acceleration = (21.0 m - 33.75 m) / (1.087 * (2.17 s)^2)
Acceleration = -3.33 m/s^2

Therefore, the car's constant deceleration before impact was -3.33 m/s^2.

b) How fast was the car traveling at impact?

To find the car's speed at impact, we can use the equation of motion that relates final velocity, initial velocity, acceleration, and time:

final velocity (v) = initial velocity (u) + acceleration (a) * time (t)

We already know the initial velocity (u), the time (t), and the acceleration (a) we found in part (a).

Plugging in the values:
final velocity (v) = 15.56 m/s + (-3.33 m/s^2) * 2.17 s

Simplify the equation:
final velocity (v) = 15.56 m/s - 7.23 m/s
final velocity (v) = 8.33 m/s

Therefore, the car was traveling at a speed of 8.33 m/s at the moment of impact.