Acceleration - free fall
How long will it take for a car to reach a speed of 180 km/h with an acceleration of 10 m/s²?
Final Answer:
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Dr. Math
To determine how long it will take for a car to reach a speed of 180 km/h with an acceleration of 10 m/s², we will use the kinematic equation for uniformly accelerated motion:
where:
- v = final velocity (in m/s),
- u = initial velocity (in m/s),
- a = acceleration (in m/s²),
- t = time (in seconds).
The final velocity is given in km/h, but we need it in m/s for consistency with the acceleration units. Convert 180 km/h to m/s:
The car starts from rest, so the initial velocity is:
The kinematic equation is:
Solve for t :
Substitute v = 50 m/s , u = 0 m/s , and a = 10 m/s² :
The car will take:
v = u + at
where:
- v = final velocity (in m/s),
- u = initial velocity (in m/s),
- a = acceleration (in m/s²),
- t = time (in seconds).
Step 1:
Convert Final Velocity to m/sThe final velocity is given in km/h, but we need it in m/s for consistency with the acceleration units. Convert 180 km/h to m/s:
v = 180 × 10003600 = 50 m/s.
Step 2:
Identify Initial VelocityThe car starts from rest, so the initial velocity is:
u = 0 m/s.
Step 3:
Rearrange the Kinematic EquationThe kinematic equation is:
v = u + at.
Solve for t :
t = v - ua.
Step 4:
Substitute Values and Solve for tSubstitute v = 50 m/s , u = 0 m/s , and a = 10 m/s² :
t = 50 - 010 = 5 seconds.
Final Answer:
The car will take:
5 seconds
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