Question

The acceleration of a particle is defined by equation, a = - 8m/s2 .
Knowing that x = 20m where t = 4s and that x = 4m where v = 16m/s,
Determine,
The time when the velocity is zero, [6]
The velocity and the total distance travelled when t = 11s [4]

Answer 1

a = -8
v = -8t+c1
x = -4t^2 + c1*t + c2
using the two data points,
when t = (c1-16)/8, v = 16
-4*16 + 4*c1 + c2 = 20
-4*((c1-16)/8)^2 + (c1-16)/8 * c1 + c2 = 4
solving those two equations, we get
c1 = 32, c2 = -44
so we have
v(t) = -8t+32
x(t) = -4t^2 + 32t - 44
Now you can answer the questions.