The point moves according to the law x (t) = t ^ 3-2t ^ 2 + t. Find v (2) and a (5)

1. If it is known by what law the point moves, and this dependence is given in the form of a function x (t), then, having calculated the first and second derivatives of the function, we find the dependences of the speed and acceleration on time:

x (t) = t ^ 3 – 2t ^ 2 + t;
v (t) = x ‘(t);
v (t) = 3t ^ 2 – 4t + 1;
a (t) = x “(t) = v ‘(t);
a (t) = 6t – 4.
2. Determine the speed and acceleration of the point for the specified times:

v (t) = 3t ^ 2 – 4t + 1;
v (2) = 3 * 2 ^ 2 – 4 * 2 + 1 = 12 – 8 + 1 = 5;
a (t) = 6t – 4;
a (5) = 6 * 5 – 4 = 30 – 4 = 26.
Answer:

v (2) = 5;
a (t) = 26.