Question

A car is stopped at a red light. When the light turns green, the car accelerates at a rate of 4 m/s² for 4 seconds. What is the final velocity of the car? How far has the car traveled. Answer

in the boxes below.
final velocity I
displacement-
m/s
m

Answer 1

The final velocity of the car is
`\(16 \, \text{m/s}\),`and the displacement is
`\(32 \, \text{m}\).`

To find the final velocity and displacement of the car, you can use the kinematic equations. The two relevant equations are:

1. Final Velocity
`(\(v_f\)):`

`\[ v_f = v_i + a \cdot t \]`

where
`\(v_i\)` is the initial velocity (assumed to be 0 m/s because the car starts from rest), \(a\) is the acceleration, and \(t\) is the time.

2. Displacement
`(\(s\)):`

`\[ s = v_i \cdot t + (1)/(2) \cdot a \cdot t^2 \]`

where
`\(v_i\)` is the initial velocity,
`\(a\)` is the acceleration, and \(t\) is the time.

Given that the car starts from rest
`(\(v_i = 0\)`), the acceleration
`(\(a\) )` is
`\(4 \, \text{m/s}^2\),` and the time (\(t\)) is \(4 \, \text{s}\), you can substitute these values into the equations.

1. Final Velocity
`(\(v_f\)):`

`\[ v_f = 0 + (4 \, \text{m/s}^2 \cdot 4 \, \text{s}) \]`

`\[ v_f = 16 \, \text{m/s} \]`

2. Displacement (\(s\)):

`\[ s = 0 \cdot 4 + (1)/(2) \cdot 4 \, \text{m/s}^2 \cdot (4 \, \text{s})^2 \]`

`\[ s = 32 \, \text{m} \]`

Therefore, the final velocity of the car is
`\(16 \, \text{m/s}\), and the displacement is \(32 \, \text{m}\).`