Let s
ct
3
, where c
1.0 m/s
3
. Compute the average
speed over the time intervals �t1
1.0 �10
�1
s, �t2
1.0
� 10
�2
s, and �t3
1.0 � 10
�3
s, with all time intervals
starting at the time t
1.0000 s. What is the instantaneous speed at t
1.0000 s
Math? Science? What?
To compute the average speed over different time intervals and the instantaneous speed at a specific time, we need to first define the equations and then use them to calculate the values.
1. Average Speed:
Average speed can be calculated by dividing the total distance traveled by the object during a given time interval by the duration of that interval. In this case, our object is moving with a constant acceleration, so the equation we'll use is:
Average Speed = (Change in distance) / (Change in time)
Given:
Initial velocity (v) at t = 1 s: v = 0.0 m/s (since the object starts from rest)
Acceleration (a): a = 1.0 m/s^2
For the time intervals:
t1 = 1.0 × 10^(-1) s
t2 = 1.0 × 10^(-2) s
t3 = 1.0 × 10^(-3) s
Using the kinematic equation for motion with constant acceleration:
v = u + at
Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
We can find the final velocity at each time interval and then calculate the average speed accordingly.
2. Instantaneous Speed:
The instantaneous speed at a specific time can be obtained by calculating the derivative of the distance traveled with respect to time at that time instant.
Given:
c3 = 3.0 m
To find the instantaneous speed at t = 1.0 s, we need to differentiate the expression for distance with respect to time and then substitute t = 1.0 s into the resulting expression.
I will now perform the calculations and provide you with the answers.