Car trouble

• Nov 26th 2008, 01:13 PM
jackiemoon
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.
• Nov 26th 2008, 03:53 PM
skeeter
Quote:

Originally Posted by jackiemoon
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