An experimental rocket car starting from rest reaches a speed of 560 km/h after a straight 450 m run on a level salt flat. Assuming that acceleration is constant, answer the following questios.
(a) What was the time of the run?
Your answer is incorrect. s
(b) What is the magnitude of the acceleration?
m/s2
change km/hr to m/s
distance=avgvelocity*time
450km/hr*1hr/3600sec * 1000m/km=125m/d
time=450m/125m/s= 3.6 seconds.
a= 125/3.6 m/s^2
To find the time of the run (a), we need to use the equation of motion for constant acceleration:
v = u + at
Where:
v is the final velocity (560 km/h),
u is the initial velocity (0 km/h, since the car starts from rest),
a is the acceleration,
t is the time.
First, we need to convert the velocities from km/h to m/s:
560 km/h = (560 * 1000) / (60 * 60) = 155.56 m/s
0 km/h = 0 m/s
We can rewrite the equation as:
t = (v - u) / a
Substituting the known values, we have:
t = (155.56 m/s - 0 m/s) / a = 155.56 m/s / a
Therefore, the time of the run (a) is given by the equation 155.56 / a.
To find the magnitude of the acceleration (b), we can rearrange the equation of motion:
v^2 = u^2 + 2as
Where:
v is the final velocity (155.56 m/s),
u is the initial velocity (0 m/s),
a is the acceleration,
s is the displacement (450 m).
Rearranging the equation, we have:
a = (v^2 - u^2) / (2s)
Substituting the known values, we have:
a = (155.56^2 m^2/s^2 - 0^2 m^2/s^2) / (2 * 450 m) = 12160 m^2/s^2 / 900 m
Therefore, the magnitude of the acceleration (b) is given by the equation 12160 / 900 m^2/s^2.
Now you can calculate the time of the run (a) and the magnitude of the acceleration (b) using the derived equations.
To determine the time of the run and the magnitude of acceleration, we can use the kinematic equation:
v = u + at
where:
v = final velocity = 560 km/h
u = initial velocity = 0 km/h (as the car starts from rest)
a = acceleration
t = time
(a) To find the time of the run:
We need to convert the velocities from km/h to m/s to ensure that the units are consistent.
Given:
v = 560 km/h,
u = 0 km/h.
Converting to m/s:
v = 560 km/h * (1000 m/1 km) * (1 h/3600 s)
= 155.56 m/s
u = 0 km/h * (1000 m/1 km) * (1 h/3600 s)
= 0 m/s
Substituting the values into the equation:
155.56 m/s = 0 m/s + a * t
Simplifying the equation, we have:
155.56 m/s = a * t
(b) To find the magnitude of the acceleration (a):
To find the acceleration, we need to rearrange the equation:
a = (v - u) / t
Substituting the values:
a = (155.56 m/s - 0 m/s) / t
Now we can solve for both t and a.