A particle is moving on a straight line in such a way that its velocity vv is given by v (t) = 2t+1v (t) = 2t+1 for 0≤t≤50≤t≤5 where tt is measured in seconds and vv in meters per second. what is the total distance traveled (in meters) by the particle between times t=0t=0 seconds and t=5t=5 seconds? (do not enter the units)

Question

Mathematics

Ms. Congeniality

15 September, 17:33

A particle is moving on a straight line in such a way that its velocity vv is given by v (t) = 2t+1v (t) = 2t+1 for 0≤t≤50≤t≤5 where tt is measured in seconds and vv in meters per second. what is the total distance traveled (in meters) by the particle between times t=0t=0 seconds and t=5t=5 seconds? (do not enter the units)

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Aisha Ortiz · Answer 1

The distance traveled by an object is calculated by multiplying the velocity and time. We are given that velocity is expressed as the equation below.

v (t) = 2t + 1

First, we multiply the given by t to get s, or the distance.

s (t) = 2t² + t

Then, we substitute t = 5.

s (t) = 2 (5²) + 5

s (t) = 55

Hence, the answer to this item is 55.