Question

The position of a particle is r(t)= (4.0t'i+ 2.4j- 5.6tk) m. (Express your answers in vector form.) (a) Determine its velocity (in m/s) and acceleration (in m/s2) as functions of time. (Use the following as necessary: t. Assume t is seconds, r is in meters, and v is in m/s, Do not include units in your answer.) v(t)= ________m/s a(t)= ________m/s2 (b) What are its velocity (in m/s) and acceleration (in m/s2) at time t 0? v(0) =_______ m/s a(0)=_______ m/s2

Answer 1

Corrected Question:

The position of a particle is r(t)= (4.0t²i+ 2.4j- 5.6tk) m. (Express your answers in vector form.)

(a) Determine its velocity (in m/s) and acceleration (in m/s²) as functions of time. (Use the following as necessary: t. Assume t is seconds, r is in meters, and v is in m/s, Do not include units in your answer.)

v(t)= ________m/s

a(t)= ________m/s²

(b) What are its velocity (in m/s) and acceleration (in m/s²) at time t 0?

v(0) =_______ m/s

a(0)=_______ m/s²

Answer:

(a)

v(t)= $8ti - 5.6k$ m/s

a(t)= 8i m/s²

(b)

v(0) = -5.6k m/s

a(0)= 8i m/s²

Explanation:

From the question, the position of the particle is given by;

r(t)= (4.0t²i+ 2.4j- 5.6tk)        -----------------(i)

(a)

(i)To get the velocity, v(t), of the particle, we'll take the first derivative of the position of the particle (given by equation (i)) with respect to time, t, as follows;

v(t) = $\frac{dr(t)}{dt}$ = $\frac{d(4.0t^2i + 2.4j - 5.6tk)}{dt}$

v(t) = $\frac{dr(t)}{dt}$ = $8ti +0j - 5.6k$

v(t) = $8ti - 5.6k$          --------------------(ii)

(ii) To get the acceleration, a(t), of the particle, we'll take the first derivative of the velocity of the particle (given by equation (ii)) with respect to time, t, as follows;

a(t) = $\frac{dv(t)}{dt}$  = $\frac{d(8ti - 5.6k)}{dt}$

a(t) = 8i                    --------------------(iii)

(b)

(i) To get the velocity of the particle at time t = 0, substitute the value of t = 0 into equation (ii) as follows;

v(t) = $8ti - 5.6k$  

v(0) = 8(0)i - 5.6k

v(0) = 0 - 5.6k

v(0) = -5.6k

(ii) To get the acceleration of the particle at time t = 0, substitute the value of t = 0 into equation (iii) as follows;

a(t) = 8i

a(0) = 8i