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Car Acceleration and Distance Travelled

Created by @nathanedwards
 at November 5th 2023, 1:13:30 am.
AP_Physics_1-Questions
#motion
#acceleration
#kinematics

Question:

A car starts from rest and accelerates uniformly at a rate of 4.0 m/s² for a time of 8.0 seconds. Determine the following:

a) The final velocity of the car. b) The distance traveled by the car during this time interval.

Answer:

a) To find the final velocity of the car, we can use the equation of motion:

v=u+a⋅t v = u + a \cdot t

where:

  • v is the final velocity,
  • u is the initial velocity (since the car starts from rest, u=0u = 0),
  • a is the acceleration, and
  • t is the time interval.

Plugging in the given values, we have:

v=0+(4.0 m/s²)⋅(8.0 s)=32 m/s v = 0 + (4.0 \, \text{m/s²}) \cdot (8.0 \, \text{s}) = 32 \, \text{m/s}

Therefore, the final velocity of the car is 32 m/s.

b) To find the distance traveled by the car, we can use another equation of motion:

s=u⋅t+12⋅a⋅t2 s = u \cdot t + \frac{1}{2} \cdot a \cdot t^2

where:

  • s is the distance traveled.

Plugging in the given values, we have:

s=0⋅(8.0 s)+12⋅(4.0 m/s²)⋅(8.0 s)2=128 m s = 0 \cdot (8.0 \, \text{s}) + \frac{1}{2} \cdot (4.0 \, \text{m/s²}) \cdot (8.0 \, \text{s})^2 = 128 \, \text{m}

Therefore, the distance traveled by the car during this time interval is 128 m.

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