Final answer:
To calculate the acceleration needed for Meghan to increase her speed from 2 m/s to 4 m/s over a distance of 5 m, we use the equation v^2 = u^2 + 2as and find that the required acceleration is 1.2 m/s².
Step-by-step explanation:
Meghan is running and wishes to increase her speed from an initial velocity was 2 m/s to accelerates to a velocity of 4 m/s over a distance of 5 m. To find out the acceleration needed to achieve this, we can use the kinematic equation:
v^2 = u^2 + 2as
where:
- v is the final velocity (4 m/s)
- u is the initial velocity (2 m/s)
- a is the acceleration
- s is the distance over which the acceleration occurs (5 m)
Rearranging the formula to solve for acceleration (a), we get:
a = (v^2 - u^2) / (2s)
Inserting the given values:
a = (4^2 - 2^2) / (2 × 5)
a = (16 - 4) / 10 = 12 / 10 = 1.2 m/s²
Therefore, Meghan's acceleration needed is 1.2 m/s² to achieve her goal.