velocity vs time graph
time (sec) displacement (m) velocity (m/s)
0 0 0
0.5 1.25 5
1 5 10
1.5 11.25 15

based on the data table, find the acceleration and then predict the velocity at the time 3.5 seconds.
a) the acceleration is 5 m/s/s and the velocity at a time of 3.5 seconds will be 35 m/s.
b) the acceleration is 10 m/s/s and the velocity at a time of 3.5 seconds will be 35 m/s.
c) the acceleration is 10 m/s/s and the velocity at a time of 3.5 seconds will be 70 m/s.
d) the acceleration is 5 m/s/s and the velocity at a time of 3.5 seconds will be 17.5 m/s.

The base of a 50-meter tower is at the origin; the base of a 50-meter tree is at (0, 50, 0). the ground is flat and the z-axis points upward. the following parametric equations describe the motion of six projectiles each launched at time t = 0 in seconds. (i) r (t) = (50 + t2)k (ii) r (t) = 2t2 j + 2t2k (iii) r (t) = 50 i + 50 j + (50 − t2)k (iv) r (t) = 2t j + (50 − t2)k (v) r (t) = (50 − 2t) i + 2t j + (50 − t)k (vi) r (t) = t i + t j + tk (a) which projectile is launched from the top of the tower and goes downward? at time t = , the projectile hits the ground at point (x, y, z) = . (b) which projectile hits the top of the tree?