What constant acceleration is required to increase the speed of a car ... What constant acceleration is required to increase the speed of a car from 25 mi/h to 50 mi/h in 4 s? (Round your answer to two decimal places.) _________________ft/s^2

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The velocity `t` hours after the start is given by

`v = 25 + at`

where `a` is the required acceleration` `.

After 4 seconds `t=4/3600` (there are 3600 seconds in an hour) we have `v = 50`

`therefore`

`25 +4/3600a = 50`

`implies a = (25(3600))/4` mi/h^2

Now, 1 mile...

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The velocity `t` hours after the start is given by

`v = 25 + at`

where `a` is the required acceleration` `.

After 4 seconds `t=4/3600` (there are 3600 seconds in an hour) we have `v = 50`

`therefore`

`25 +4/3600a = 50`

`implies a = (25(3600))/4` mi/h^2

Now, 1 mile = 5280 feet so

` ``a = (25/4)(3600)(5280)` ft/h^2

`= 25/4(5280/3600)` ft/s^2 (3600^2 hours squared in a second squared)

Therefore a = 9.17 ft/s^2

Approved by eNotes Editorial Team