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Math Help - Car trouble

  1. #1
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    Car trouble

    Hi,

    Can anybody help with the following please:

    A car can reach a speed of 100km/h in 7 seconds starting at rest and accelerating uniformly (at its maximum acceleration rate). The maximum braking rate of a car (i.e. the highest negative acceleration at which it can reduce its speed) is 8 m/sē. Find the minimum time in which the car can cover a distance of 1km if it starts and ends at rest.

    I'm stumped on this one - I think my brain is broken.

    Thanks in advance for any ideas/assistance.
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  2. #2
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    Quote Originally Posted by jackiemoon View Post
    Hi,

    Can anybody help with the following please:

    A car can reach a speed of 100km/h in 7 seconds starting at rest and accelerating uniformly (at its maximum acceleration rate). The maximum braking rate of a car (i.e. the highest negative acceleration at which it can reduce its speed) is 8 m/sē. Find the minimum time in which the car can cover a distance of 1km if it starts and ends at rest.

    I'm stumped on this one - I think my brain is broken.

    Thanks in advance for any ideas/assistance.
    100 km/hr = 250/9 m/s

    a = (250/9 m/s)/(7 s) = 250/63 m/s^2

    distance traveled while speeding up = (1/2)at^2 = (1/2)(250/63)(49) meters

    distance traveled at the constant 100 km/hr = (250/9)t meters

    distance traveled while slowing down = (1/2)(250/72)(64) meters

    add up the three distances, set equal to 1000 m, solve for t.

    total time = t + 15 sec
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