4. A car accelerates at 0.5 m/s2 starting from rest.
a. After 4 s what is its velocity?
b. After 4 s, how far has it traveled from its starting position?
a. V = a*t = 0.5m/s^2 * 4s. = 2 m/s.
b. d = 0.5a*t^2 = 0.5*0.5*4^2 = 4 m.
To find the answers to these questions, we can use the formulas of kinematics, which describe the motion of objects. The key formulas here are:
1. Velocity formula: v = u + at
2. Displacement formula: s = ut + (1/2)at^2
Where:
- v represents the final velocity,
- u represents the initial velocity (which is 0 in this case since the car starts from rest),
- a represents the acceleration, and
- t represents time.
a. After 4 seconds, to find the velocity of the car, we can use the velocity formula. Substituting the values into the formula:
v = u + at
= 0 + (0.5 m/s^2)(4 s)
= 0 + 2 m/s
= 2 m/s
Therefore, the car's velocity after 4 seconds is 2 m/s.
b. To find the distance the car has traveled from its starting position after 4 seconds, we can use the displacement formula. Substituting the values into the formula:
s = ut + (1/2)at^2
= 0 + (1/2)(0.5 m/s^2)(4 s)^2
= 0 + (1/2)(0.5 m/s^2)(16 s^2)
= 0 + 4 m
= 4 m
Therefore, the car has traveled a distance of 4 meters from its starting position after 4 seconds.