Applications of Integration: Displacement, Velocity, and Acceleration

Distance and Displacement

4 Activities

The acceleration due to gravity of an object is given by a(t)=−9.8a\left(t\right)=-9.8a(t)=−9.8. If the initial velocity and displacement are given by v(0)=5v\left(0\right)=5v(0)=5 and d(0)=2d\left(0\right)=2d(0)=2, find the function that represents the displacement at time t.

d(t)=−4.9t2+5t+2d\left(t\right)=-4.9t^2+5t+2d(t)=−4.9t2+5t+2

d(t)=−4.9t2−5t+2d\left(t\right)=-4.9t^2-5t+2d(t)=−4.9t2−5t+2

d(t)=−9.8t+2d\left(t\right)=-9.8t+2d(t)=−9.8t+2

d(t)=−9.8t2+5t+2d\left(t\right)=-9.8t^2+5t+2d(t)=−9.8t2+5t+2

d(t)=−9.8t2−5t+2d\left(t\right)=-9.8t^2-5t+2d(t)=−9.8t2−5t+2

I don't know

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-8v(t)=t2−2t−8
For the time interval 1≤t≤61 \leq t \leq 61≤t≤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)=-9.8a(t)=−9.8. If the initial velocity and displacement are given by v(0)=5v\left(0\right)=5v(0)=5 and d(0)=2d\left(0\right)=2d(0)=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-8v(t)=t2−2t−8
For the time interval 1≤t≤61 \leq t \leq 61≤t≤6, find (a) the displacement of the particle and (b) the distance traveled by the particle.

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.

The graph of f(x)f(x)f(x) is given below. What is the total distance given by f(x)f\left(x\right)f(x) from x=0 x=0\ x=0  to x=4x=4x=4?

A train travels at (t+1) m/s(t+1) \space m/s(t+1) 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-8v(t)=t2−2t−8
For the time interval 1≤t≤61 \leq t \leq 61≤t≤6, find (a) the displacement of the particle and (b) the distance traveled by the particle.

Applications of Integration: Displacement, Velocity, and Acceleration

Related Topics

Distance and Displacement

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Applications of Integration: Finding distance and displacement

Applications of Integration: Displacement, Velocity, and Acceleration

Applications of Integration: Finding distance and displacement

Kinematics

Applications of Integration: Finding distance and displacement