Calculate velocity and acceleration if position vector r is given.
We used here bold face letters to indicate vectors.
An object is moving so that its position is given by the vector
r = 10t i + (100 - 4.905 t2) j (1)
where t is time of motion. What is the expression for velocity and acceleration of this object? Describe what type of motion it is.
We remind you the meaning of i, j, and k
i - a unit vector along the x axis
j - a unit vector along the y axis
k - a unit vector along the z axis
Solution.
Velocity is a first derivative of position with respect to time
v = dr/dt = 10 i – 2.0*4.905t = 10 i – 9.81t j (2)
Acceleration is the second derivative of position with respect to time or – first derivative of velocity with respect to time.
a = dv/dt = -9.8 j (3)
It is a projectile motion. An object was launched 100m above the origin of y axis, with velocity 10m/s in the direction of the x axis. Its acceleration is equal to gravities acceleration and directed in the negative direction of the y axis.