All MCAT Physical Resources
Example Questions
Example Question #11 : Motion In One Dimension
A child throws a ball straight up into the air. He throws the ball with an initial velocity of . Assume there is no air resistance.
How long will it take for the ball to reach a velocity of , while in the air?
The baseball will never have a velocity of .
In order to solve for the time at which the ball has a velocity of , we need to use an equation which incorporates all of the known variables. We know the acceleration due to gravity, the initial velocity, and the final velocity. As a result, the best equation to use is the one that allows us to simply solve for the unknown variable, time.
Keep in mind that 1.6s is also a time at which the velocity is , but this time refers to the point when the boy catches the ball. The question asks for the specific time while the ball is still in the air, so the correct answer, 0.8s, refers to the point where the ball is at its peak height.
Example Question #1 : Calculating Motion In One Dimension
If a 15kg ball takes five seconds to strike the ground when released from rest, at what height was the ball dropped?
50m
250m
100m
75m
125m
125m
Using the equation we can find the distance at which the ball was dropped. Notice that the mass of the ball does not matter in this problem. We are told that the ball is dropped from rest making, , thus we have . When we plug in our values, and assuming that acceleration is equal to gravity (10m/s2) we find that = 125m.
Example Question #2 : Calculating Motion In One Dimension
How far will an object travel after ten seconds if it is dropped into a bottomless pit?
50m
500m
25m
300m
250m
500m
Since the object is dropped, the inital velocity is zero. Gravity is the only acceleration, the time is ten seconds, and the distance at which the object travels is unknown.
The equation can be used to find the distance traveled.
Example Question #1 : Motion In One Dimension
How long does it take an object to travel a distance of 30m from rest at a constant acceleration of 2m/s2?
Using the equation , we can solve for time.
Since the object started at rest, . Now we are left with the equation .
Plugging in the remaining values we can find that t = 5.5s.
Example Question #261 : Mcat Physical Sciences
A car is moving with a constant velocity of when it abruptly stops, applying a constant breaking acceleration of . Over what distance does the car come to a stop?
This problem can be easily solved using the formula, , and solving for . Our initial velocity is , acceleration is , and final velocity is .
The car comes to a stop after applying the breaks over 10m.
Example Question #262 : Mcat Physical Sciences
A sprinter running a race accelerates constantly at from rest. What is his approximate final velocity as he crosses the finish line?
To answer this question, we must have a solid understanding of the kinematics equations. For this question, we must use an equation relating final velocity, distance, and acceleration.
The best fit for this is .
Since we are solving for final velocity, and we started from rest, we can simplify the equation.
Example Question #261 : Mcat Physical Sciences
An car accelerates from rest and travels in . What is the approximate acceleration of the car?
The kinematics equation relating distance, time, and acceleration is .
Since we know that the car was initially at rest, we can rewrite the equation with zero initial velocity.
Now we can plug in our values from the question, and solve for the acceleration.
Example Question #261 : Mcat Physical Sciences
If an ball is dropped from a cliff high, how long will it take the ball to strike the ground?
Since acceleration is constant, we can use the appropriate kinematics equation to solve:
We are given the height of the cliff, which will be equal to the distance traveled. The initial velocity is zero since the ball starts from rest and the acceleration will be equal to the acceleration due to gravity. Use these values to calculate the time.
Example Question #31 : Translational Motion
A 2kg mass is suspended on a rope that wraps around a frictionless pulley. The pulley is attached to the ceiling and has a mass of 0.01kg and a radius of 0.25m. The other end of the rope is attached to a massless suspended platform, upon which 0.5kg weights may be placed. While the system is initially at equilibrium, the rope is later cut above the weight, and the platform subsequently raised by pulling on the rope.
What is the velocity of the platform two seconds after the rope is cut?
Think back to the 3 main kinematics equations that we know.
vf2 = vi2 + 2aΔx
vf = vi + at
Δx = vit + ½at2
We need to determine which formula will allow us to find final velocity after a given amount of time.
vf = vi + at = (0m/s) + (9.8m/s2)(2s) = 19.6m/s
Example Question #32 : Translational Motion
If an object is dropped from a height of 450 meters above Earth, what is its velocity just before impact?
95m/s
45m/s
6.7m/s
67m/s
95m/s
First calculate the time it takes to hit the ground using the equation .
We can plug in values (including acceleration due to gravity) and solve for t.
t = 9.49s
Next, find the final velocity with the equation .
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