A car starts from rest and travels for 5.2 s with a uniform acceleration of +1.8 m/s2. The driver then applies the brakes, causing a uniform acceleration of -2.0 m/s2. The breaks are applied for 2.00 s.
(a) How fast is the car going at the end of the braking period?
Fast Five
To find the speed of the car at the end of the braking period, we need to calculate the change in velocity during this time.
First, let's find the initial velocity after the first 5.2 seconds of acceleration. The formula for calculating the velocity with a uniform acceleration is given by:
v = u + at
Where:
v = final velocity
u = initial velocity (which is 0 in this case, as the car starts from rest)
a = acceleration
t = time
For the first acceleration phase:
u = 0
a = 1.8 m/s^2
t = 5.2 s
v = 0 + (1.8 m/s^2) * (5.2 s)
v = 9.36 m/s
Now, let's find the final velocity after the braking period. Again, using the same formula:
u = 9.36 m/s (velocity after the first 5.2 seconds)
a = -2.0 m/s^2
t = 2.0 s
v = 9.36 m/s + (-2.0 m/s^2) * (2.0 s)
v = 9.36 m/s - 4.0 m/s
v = 5.36 m/s
Therefore, the car is going at a speed of 5.36 m/s at the end of the braking period.
To find the speed of the car at the end of the braking period, we need to calculate the final velocity after the acceleration and braking phases.
First, let's calculate the final velocity after the acceleration phase. We can use the formula:
v = u + at
where:
v is the final velocity,
u is the initial velocity,
a is the uniform acceleration, and
t is the time.
Given:
u = 0 m/s (as the car starts from rest)
a = 1.8 m/s^2
t = 5.2 s
Using the formula, we have:
v = 0 + (1.8 m/s^2) * (5.2 s)
v = 0 + 9.36 m/s
v = 9.36 m/s
Now, let's calculate the final velocity after the braking phase. Again, we can use the same formula:
v = u + at
where:
v is the final velocity,
u is the initial velocity,
a is the uniform acceleration (in the opposite direction, as it's braking), and
t is the time.
Given:
u = 9.36 m/s (as this is the velocity after the acceleration phase)
a = -2.0 m/s^2 (note the negative sign since it's braking)
t = 2.00 s
Using the formula, we have:
v = 9.36 m/s + (-2.0 m/s^2) * (2.00 s)
v = 9.36 m/s - 4.00 m/s
v = 5.36 m/s
Therefore, the car is going at a speed of 5.36 m/s at the end of the braking period.