# Thread: Projectile Motion - Vector

1. ## Projectile Motion - Vector

The velocity of a particle moving in the xy plane is given by = (5.2 t - 4.8 t2) + 8.0, with in meters per second and t (> 0) in seconds. (a) What is the acceleration when t = 2.3 s? (b) When (if ever) is the acceleration zero? (c) When (if ever) does the speed equal 10 m/s?

I am able to solve for (a) and (b), but (c) gives me complex numbers as a result of the quadratic equation.

Would the answer for (c) be never?

Thanks!

2. Hello silencecloak
Originally Posted by silencecloak
The velocity of a particle moving in the xy plane is given by = (5.2 t - 4.8 t2) + 8.0, with in meters per second and t (> 0) in seconds. (a) What is the acceleration when t = 2.3 s? (b) When (if ever) is the acceleration zero? (c) When (if ever) does the speed equal 10 m/s?

I am able to solve for (a) and (b), but (c) gives me complex numbers as a result of the quadratic equation.

Would the answer for (c) be never?

Thanks!
I suspect you forgot the $\displaystyle \pm$ sign in part (c).

Speed = $\displaystyle \sqrt{(5.2t-4.8t^2)^2+64}=10$

$\displaystyle \Rightarrow (5.2t-4.8t^2)^2=36$

$\displaystyle \Rightarrow 5.2t-4.8t^2=\color{red}\pm\color{black}6$

Taking the - sign gives a real, positive root, which (if my arithmetic is correct) is $\displaystyle t = 1.78$