Need help a simple question: When a car is braking, the distance of m it travels after the brakes are applied until it stop...

[chunwai]

When a car is braking, the distance of m it travels after the brakes are applied until it stops consists of two parts: one part varies directly as the time t seconds after the brakes are applied, the other part varies directly as the square of t. If the distance travelled by the car are 60m and 75m when t=2 and t=3 respectively, find the distance it travels when t=4. How to calculate the answer 80?

 

[tkhunny]

d₁ Varies Directly with t: d₁ = kt, for some constant 'k'.
d₂ Varies Directly with the square of t: d₂ = mt^2, for some constant 'm'.
d = d₁ + d₂

Go! I mean , "stop".

 

[HallsofIvy]

"When a car is braking, the distance of m it travels after the brakes are applied until it stops consists of two parts: one part varies directly as the time t seconds after the brakes are applied, the other part varies directly as the square of t."
So d= at+ bt^2.

"the distance travelled by the car are 60m and 75m when t=2 and t=3 respectively,"
60= 2a+ 4b and 75= 3a+ 9b. Solve those two equations for a and b.

"find the distance it travels when t=4."
Evaluate 4a+ 16b for the a and b you got before.