Question

A swimmer speeds up from 1.1 m/s to 1.5 m/s by accelerating at 0.1m/s² during the last stages of the race. How long did it take the to achieve this change in speed?

Answer 1

We can solve this problem using the equation:

v_f = v_i + a*t

where v_f is the final velocity, v_i is the initial velocity, a is the acceleration, and t is the time it takes to achieve the change in speed.

Given:

v_i = 1.1 m/s

v_f = 1.5 m/s

a = 0.1 m/s²

Substituting the values into the equation, we get:

1.5 m/s = 1.1 m/s + 0.1 m/s² * t

Simplifying the equation, we get:

0.4 m/s = 0.1 m/s² * t

Dividing both sides by 0.1 m/s², we get:

t = 4 seconds

Therefore, it took the swimmer 4 seconds to achieve the change in speed from 1.1 m/s to 1.5 m/s.

Answer 2

To solve the problem, we can use the following kinematic equation:

v = u + at

where:

v = final velocity = 1.5 m/s

u = initial velocity = 1.1 m/s

a = acceleration = 0.1 m/s²

t = time taken

Substituting the values, we get:

1.5 = 1.1 + (0.1)t

Simplifying the equation, we get:

0.4 = 0.1t

t = 4 seconds

Therefore, it took the swimmer 4 seconds to achieve the change in speed.