Question
A sprinter enters the 60m mark of the race with a velocity of 10.2m^-1. He continued to accelerate at a rate of 2.1ms^-2 over the next 10m covering this in 0.81s. Calculate the velocity of the sprinter when he reached 70m
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Answer to a math question A sprinter enters the 60m mark of the race with a velocity of 10.2m^-1. He continued to accelerate at a rate of 2.1ms^-2 over the next 10m covering this in 0.81s. Calculate the velocity of the sprinter when he reached 70m
Jayne
4.4106 Answers
To calculate the final velocity of the sprinter when he reaches 70m, we can use the equation of motion:
v^2 = u^2 + 2as
Where:
- v is the final velocity
- u is the initial velocity
- a is the acceleration
- s is the displacement
Given:
- Initial velocity (u) = 10.2 m/s
- Acceleration (a) = 2.1 m/s^2
- Displacement (s) = 70 m - 60 m = 10 m
Substituting the given values into the equation, we have:
v^2 = (10.2 m/s)^2 + 2 * 2.1 m/s^2 * 10 m
Calculating this equation:
v^2 = 104.04 m^2/s^2 + 42 m^2/s^2
v^2 = 146.04 m^2/s^2
To find the final velocity (v), we take the square root of both sides:
v = √(146.04 m^2/s^2)
v ≈ 12.08 m/s (rounded to 2 decimal places
Therefore, the velocity of the sprinter when he reaches 70m is approximately 12.08 m/s
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