Questions: A race car has a speed of 98 m / s. The driver hits the brakes, causing the car to slow down at a constant rate of 12 m / s^2 for a period of 8 seconds. Compute the speed of the car at 2 s, 4 s, 6 s, and 8 s after the driver hits the brakes, The speed of the car at 2 s is m / s, The speed of the car at 4 s is m/s. The speed of the car at 6 s is m / s. The speed of the car at 8 s is m / s.

A race car has a speed of 98 m / s. The driver hits the brakes, causing the car to slow down at a constant rate of 12 m / s^2 for a period of 8 seconds.
Compute the speed of the car at 2 s, 4 s, 6 s, and 8 s after the driver hits the brakes,
The speed of the car at 2 s is m / s,
The speed of the car at 4 s is m/s.
The speed of the car at 6 s is m / s.
The speed of the car at 8 s is m / s.

Transcript text: A race car has a speed of $98 \mathrm{~m} / \mathrm{s}$. The driver hits the brakes, causing the car to slow down at a constant rate of $12 \mathrm{~m} / \mathrm{s}^{2}$ for a period of 8 seconds. Compute the speed of the car at $2 \mathrm{~s}, 4 \mathrm{~s}, 6 \mathrm{~s}$, and 8 s after the driver hits the brakes, The speed of the car at 2 s is $\square$ $\square$ $\mathrm{m} / \mathrm{s}$, The speed of the car at 4 s is $\square$ m's. The speed of the car at 6 s is $\square$ $\mathrm{m} / \mathrm{s}$. The speed of the car at 8 s is $\square$ $\mathrm{m} / \mathrm{s}$.

Solution

Solution Steps

Step 1: Identify the initial conditions and given data

The initial speed of the race car is $ v_0 = 98 \, \mathrm{m/s} $. The car decelerates at a constant rate of $ a = -12 \, \mathrm{m/s^2} $. We need to find the speed of the car at $ t = 2 \, \mathrm{s}, 4 \, \mathrm{s}, 6 \, \mathrm{s}, $ and $ 8 \, \mathrm{s} $.

Step 2: Use the kinematic equation for velocity

The kinematic equation for velocity under constant acceleration is: \[ v = v_0 + at \]

Step 3: Calculate the speed at $ t = 2 \, \mathrm{s} $

Substitute $ v_0 = 98 \, \mathrm{m/s} $, $ a = -12 \, \mathrm{m/s^2} $, and $ t = 2 \, \mathrm{s} $ into the equation: \[ v = 98 + (-12)(2) \] \[ v = 98 - 24 \] \[ v = 74 \, \mathrm{m/s} \]

Step 4: Calculate the speed at $ t = 4 \, \mathrm{s} $

Substitute $ v_0 = 98 \, \mathrm{m/s} $, $ a = -12 \, \mathrm{m/s^2} $, and $ t = 4 \, \mathrm{s} $ into the equation: \[ v = 98 + (-12)(4) \] \[ v = 98 - 48 \] \[ v = 50 \, \mathrm{m/s} \]

Step 5: Calculate the speed at $ t = 6 \, \mathrm{s} $

Substitute $ v_0 = 98 \, \mathrm{m/s} $, $ a = -12 \, \mathrm{m/s^2} $, and $ t = 6 \, \mathrm{s} $ into the equation: \[ v = 98 + (-12)(6) \] \[ v = 98 - 72 \] \[ v = 26 \, \mathrm{m/s} \]

Step 6: Calculate the speed at $ t = 8 \, \mathrm{s} $

Substitute $ v_0 = 98 \, \mathrm{m/s} $, $ a = -12 \, \mathrm{m/s^2} $, and $ t = 8 \, \mathrm{s} $ into the equation: \[ v = 98 + (-12)(8) \] \[ v = 98 - 96 \] \[ v = 2 \, \mathrm{m/s} \]