Question

You ride your bike to school. As you approach an intersection, you decrease your speed by 1.5 miles per hour per second. Select an inequality that represents the time tt (in seconds) until your speed decreases by more than 10.5 miles per hour. Then solve the inequality.

Answer 1

The acceleration is equal to the change in velocity per time. Now, the acceleration is said to be 1.5 miles/h·s. We are asked to find the corresponding time when the change in velocity is 10.5 miles/h such that the acceleration does not change.

a = Δv/t
1.5 = 10.5/t
t = 7 seconds

Answer 2

The time elapsed is greater than 7 seconds

Explanation:

From definition

acceleration = change in speed/time elapsed

or:

a = Δv/t

Rearranging:

a*t = Δv

If your speed decreases by more than 10.5 miles per hour, then:

Δv > 10.5

Replacing with the previous equation and solving for t:

a*t > 10.5

t > 10.5/1.5

t > 7 s