starting from rest, a car accelerates at a constant rate of 3 m/s^2for a time of 5 s;
a. compute the velocity of the car at 1 s, 2 s,3 s, 4 s, and 5 s and plot these velocity values against time.
b. compute the distance traveled by the car for these same times and plot distance values against time.
v = 3 t
x = 1.5 t^2
To compute the velocity of the car at different times and plot the values, we can use the equations of linear motion. The equation that relates velocity, acceleration, and time is:
v = u + a * t
Where:
v is the final velocity
u is the initial velocity (which is 0 m/s since the car starts from rest)
a is the acceleration (3 m/s^2 in this case)
t is the time elapsed
Let's calculate the velocity at 1s, 2s, 3s, 4s, and 5s using the given acceleration and plot these values against time:
1) Velocity at 1s:
v = 0 + 3 * 1 = 3 m/s
2) Velocity at 2s:
v = 0 + 3 * 2 = 6 m/s
3) Velocity at 3s:
v = 0 + 3 * 3 = 9 m/s
4) Velocity at 4s:
v = 0 + 3 * 4 = 12 m/s
5) Velocity at 5s:
v = 0 + 3 * 5 = 15 m/s
Plotting these velocity values against time will show how the velocity of the car changes over the given time period.
To compute the distance traveled by the car at different times and plot the distance values against time, we will use the equation that relates distance, initial velocity, acceleration, and time:
s = u * t + (1/2) * a * t^2
Where:
s is the distance traveled
Let's calculate the distance traveled by the car at 1s, 2s, 3s, 4s, and 5s using the given acceleration and plot these values against time:
1) Distance at 1s:
s = 0 * 1 + (1/2) * 3 * 1^2 = 1.5 m
2) Distance at 2s:
s = 0 * 2 + (1/2) * 3 * 2^2 = 6 m
3) Distance at 3s:
s = 0 * 3 + (1/2) * 3 * 3^2 = 13.5 m
4) Distance at 4s:
s = 0 * 4 + (1/2) * 3 * 4^2 = 24 m
5) Distance at 5s:
s = 0 * 5 + (1/2) * 3 * 5^2 = 37.5 m
Plotting these distance values against time will show how the distance traveled by the car increases over the given time period.