High School
SAT
ACT
University
MCAT
LSAT
DAT

Applications of Integration: Position, Velocity and Acceleration

Related Topics

Wize University Calculus 1 Textbook > Applications of Integration for Physical Science

Position, Velocity, and Acceleration

4 Activities

A sky diver with a broken parachute falls at a constant acceleration
of −10 m/s2-10 \ m/s^2. He passes a bird at 1000 m1000 \ m of altitude at a speed of 100 m/s100\ m/s.

(a) How fast is he moving 1010 seconds later?
(b) Has he hit the ground yet? This may change your answer to part (a).
More Position, Velocity, and Acceleration Questions:
Applications of Integration: Position from Acceleration
The position of an object is given by x(t)x(t). If its acceleration is given by a(t)=6t−2a(t)=6t-2 m/s2 and if it starts from x(0)=1x(0)=1 m with a velocity v(0)=2v(0)=2m/s, where will the object be at t=2t=2?
Applications of Integration: Position from Acceleration
The position of an object is given by x(t)x(t). If its acceleration is given by a(t)=6t−2a(t)=6t-2 m/s2 and if it starts from x(0)=1x(0)=1 m with a velocity v(0)=2v(0)=2m/s, where will the object be at t=2t=2?
A clown is shot directly up out of a cannon with a velocity of 50 m/s50\ m/s. If gravity causes a −10 m/s2-10 \ m/s^2 constant acceleration, how high is the clown 22 seconds later?
Applications of Integration: Position, Velocity and Acceleration
Suppose a car hits the brakes at full power and comes to a complete stop after 50 meters. Assuming that the deceleration caused by the brakes is a constant −10 m/sec2-10 \text{ m/sec}^2, find the speed of the car (in meters per second, to two decimal places) when it began braking.
Applications of Integrals: Position, Velocity and Acceleration
Suppose a coin is dropped off the side of a 50 meter tall cliff. Find the speed of the coin when it hits the ground (to two decimal places) in meters per second.
Applications of Integration: Position, Velocity and Acceleration
If an object is dropped off a 100-meter cliff, find its average velocity (to two decimal places) over the time it is dropped to the time it hits the ground.
Applications of Integration: Position from Acceleration
The position of an object is given by x(t)x(t). If its acceleration is given by a(t)=6t−2a(t)=6t-2 m/s2 and if it starts from x(0)=1x(0)=1 m with a velocity v(0)=2v(0)=2m/s, where will the object be at t=2t=2?
Kinematics
The following graph represents the velocity of a particle in m/s, find the total displacement in meters of the particle from t=0 to t=5.
Related Rates
A clown is shot directly up out of a cannon with a velocity of
50 m/s50\ m/s. If gravity causes a −10 m/s2-10 \ m/s^2 constant acceleration, how high is the clown 22 seconds later?