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Wize University Calculus 1 Textbook > Applications of Integration

Distance and Displacement

4 Activities

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

Position, Velocity, and Acceleration

4 Activities

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.



More Distance and Displacement Questions:
Applications of Integration: Finding distance and displacement
The velocity function, in meters per second, of a particle moving along a line is given by
v(t)=t2−2t−8v(t)=t^2-2t-8
For the time interval 1≤t≤61 \leq t \leq 6, find (a) the displacement of the particle and (b) the distance travelled by the particle.
Applications of Integration: Displacement, Velocity, and Acceleration
The acceleration due to gravity of an object is given by a(t)=−9.8a\left(t\right)=-9.8. If the initial velocity and displacement are given by v(0)=5v\left(0\right)=5 and d(0)=2d\left(0\right)=2, find the function that represents the displacement at time t.
Applications of Integration: Finding distance and displacement
The velocity funciton, in meters per second, of a particle moving alone a line is given by
v(t)=t2−2t−8v(t)=t^2-2t-8
For the time interval 1≤t≤61 \leq t \leq 6, find (a) the displacement of the particle and (b) the distance traveled by the particle.
The graph of f(x)f(x) is given below. What is the total distance given by f(x)f\left(x\right) from x=0 x=0\ to x=4x=4?
A train travels at (t+1) m/s(t+1) \space m/s. How far does it travel after 4 seconds?
Applications of Integration: Finding distance and displacement
The velocity funciton, in meters per second, of a particle moving alone a line is given by
v(t)=t2−2t−8v(t)=t^2-2t-8
For the time interval 1≤t≤61 \leq t \leq 6, find (a) the displacement of the particle and (b) the distance traveled by the particle.
Applications of Integration: Displacement, Velocity, and Acceleration
The acceleration due to gravity of an object is given by a(t)=−9.8a\left(t\right)=-9.8. If the initial velocity and displacement are given by v(0)=5v\left(0\right)=5 and d(0)=2d\left(0\right)=2, find the function that represents the displacement at time t.
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?
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?
Applications of Integration: Position, Velocity and Acceleration
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?