In a test run, a certain car accelerates uniformly from zero to 17 m/s in 2.95s.
a.) what is the magnitude of the car's acceleration?
b.) how long does it take the car to change it's speed from 8.5m/s to 17m/s?
c.) will doubling the time always double the change in speed?
a=changevelociyt/time
time=changevelocity/a
velocity=vi+at no
To find the answers to these questions, we will use the formulas of uniform acceleration, which are:
a = (vf - vi) / t
where:
a = acceleration,
vf = final velocity,
vi = initial velocity,
t = time.
Let's solve the questions step by step:
a.) What is the magnitude of the car's acceleration?
In the given problem, the initial velocity (vi) is 0 m/s, and the final velocity (vf) is 17 m/s. The time (t) is given as 2.95 seconds. We can use the formula to calculate the acceleration (a):
a = (17 m/s - 0 m/s) / 2.95 s
a = 17 m/s / 2.95 s
a ≈ 5.76 m/s²
Therefore, the magnitude of the car's acceleration is approximately 5.76 m/s².
b.) How long does it take the car to change its speed from 8.5 m/s to 17 m/s?
To solve this question, we need to rearrange the formula to solve for time (t):
t = (vf - vi) / a
Here, the initial velocity (vi) is 8.5 m/s, the final velocity (vf) is 17 m/s, and we already know the acceleration (a) from the previous question.
t = (17 m/s - 8.5 m/s) / 5.76 m/s²
t = 8.5 m/s / 5.76 m/s²
t ≈ 1.47 s
Therefore, it takes approximately 1.47 seconds for the car to change its speed from 8.5 m/s to 17 m/s.
c.) Will doubling the time always double the change in speed?
No, doubling the time will not always double the change in speed. The change in speed is determined by the acceleration (a) of the car. If the acceleration remains constant, then doubling the time will double the change in speed.
However, if the acceleration changes during the time interval, then the change in speed will not double even if the time is doubled. The rate at which the car's speed changes depends on the acceleration, and doubling the time will only have a proportional effect on the change in speed if the acceleration remains constant.