A car is speeding up and has an instantaneous velocity of 1.0 m/s in the +x-direction when a stopwatch reads 10.0 s. It has a constant acceleration of 2.0 m/s2 in the +x-direction.
(a) What change in speed occurs between t = 10.0 seconds and t = 13.0 s?
To find this, we can use the formula for final velocity (v) given acceleration (a), initial velocity (v_0), and time (t):
v = v_0 + a*t
First, we need to find the speed at t = 13.0 s:
v_13 = v_0 + a * (13.0s - 10.0s)
v_13 = 1.0 m/s + (2.0 m/s^2) * 3.0s
v_13 = 1.0 m/s + 6.0 m/s = 7.0 m/s
Now we can find the change in speed between t = 10.0 seconds and t = 13.0 s:
Δv = v_13 - v_10
Δv = 7.0 m/s - 1.0 m/s
Δv = 6.0 m/s
The change in speed between t = 10 seconds and t = 13 seconds is 6.0 m/s in the +x-direction.
To find the change in speed between t = 10.0 s and t = 13.0 s, we can use the kinematic equation:
Vf = Vi + at
where:
Vf is the final velocity
Vi is the initial velocity
a is the acceleration
t is the time interval
Based on the given information:
Initial velocity (Vi) = 1.0 m/s
Acceleration (a) = 2.0 m/s^2
Time interval (Δt) = 13.0 s - 10.0 s = 3.0 s
To find the final velocity (Vf), we substitute the given values into the equation:
Vf = Vi + at
Vf = 1.0 m/s + (2.0 m/s^2)(3.0 s)
Vf = 1.0 m/s + 6.0 m/s
Vf = 7.0 m/s
Therefore, the change in speed between t = 10.0 s and t = 13.0 s is 7.0 m/s - 1.0 m/s = 6.0 m/s.
To calculate the change in speed of the car between t = 10.0 s and t = 13.0 s, we first need to find the final velocity at t = 13.0 s and subtract the initial velocity at t = 10.0 s.
Given information:
- Initial velocity at t = 10.0 s: 1.0 m/s in the +x-direction
- Constant acceleration: 2.0 m/s^2 in the +x-direction
To find the final velocity at t = 13.0 s, we can use the equation:
vf = vi + at
where:
- vf is the final velocity
- vi is the initial velocity
- a is the acceleration
- t is the time interval
Substituting the given values, we have:
vf = 1.0 m/s + (2.0 m/s^2)(13.0 s - 10.0 s)
= 1.0 m/s + (2.0 m/s^2)(3.0 s)
= 1.0 m/s + 6.0 m/s
= 7.0 m/s
The final velocity at t = 13.0 s is 7.0 m/s in the +x-direction.
Now, to find the change in speed, we subtract the initial velocity from the final velocity:
Change in speed = vf - vi
= 7.0 m/s - 1.0 m/s
= 6.0 m/s
Therefore, the change in speed that occurs between t = 10.0 s and t = 13.0 s is 6.0 m/s.