a car can accelerate at 16 m/s^2. It races against another car which travels at 12 m/s^2. The car that travels at 12 m/s^2 leaves 1 second earlier. Find the time it takes to the first car to overtake the 2nd car and the distance they travel before they are side by side.
I attempted this question but now know if I did it correctly.
using the equation d = v1t + 1/2at^2
I get 1/2*16t^2 = 1/2*12(t+1)^2
which simplifies to t^2-6t-3=0
using the quadratic formula I get t = 6.5 or t = -0.46 however time can't be negative.
therefore, it takes the 1st car 6.5 seconds to overtake the 2nd car.
subing time into the distance formula
d = 0(6.5) + 1/2(16)(6.5)^2
d = 338
checking the distance with the other car
d = 0(7.5) + 1/2(12)(7.5)^2
d = 337.5
therefore, they travel 338 m before they are side by side
I attempted this question but now know if I did it correctly.
using the equation d = v1t + 1/2at^2
I get 1/2*16t^2 = 1/2*12(t+1)^2
which simplifies to t^2-6t-3=0
using the quadratic formula I get t = 6.5 or t = -0.46 however time can't be negative.
therefore, it takes the 1st car 6.5 seconds to overtake the 2nd car.
subing time into the distance formula
d = 0(6.5) + 1/2(16)(6.5)^2
d = 338
checking the distance with the other car
d = 0(7.5) + 1/2(12)(7.5)^2
d = 337.5
therefore, they travel 338 m before they are side by side