A car is stopped at a traffic light. The light changes to green and the driver starts to drive, accelerating at a rate of 4 m/s^2. Write an equation for the distance the car travels in time.
d = 0.5*a*t^2.
To find the equation for the distance the car travels in time, we can use the kinematic equation for uniformly accelerated motion:
\[d = ut + \frac{1}{2}at^2\]
where:
- \(d\) is the distance traveled
- \(u\) is the initial velocity (which is 0 since the car starts from rest)
- \(t\) is the time taken
- \(a\) is the acceleration
Since the car is initially stopped, the initial velocity (\(u\)) is 0 m/s. The acceleration (\(a\)) is given as 4 m/s².
Therefore, the equation for the distance the car travels in time (\(t\)) is:
\[d = \frac{1}{2} \times 4 \times t^2\]
which simplifies to:
\[d = 2t^2\]
To find the equation for the distance traveled by the car in time, we first need to use a formula of motion called the kinematic equation. The equation that relates distance (d), initial velocity (v₀), time (t), and acceleration (a) is given by:
d = v₀t + (1/2)at²
In this case, since the car is starting from rest, the initial velocity (v₀) would be 0 m/s. Additionally, the acceleration (a) is given as 4 m/s². Therefore, the equation becomes:
d = (0)t + (1/2)(4)t²
Simplifying the equation gives us the final answer:
d = 2t²