Question 14 of 18intermediate🔧 ApplyNumerical5 marks
The position of a particle is given by r = 3.0t i - 2. j + 4.0 k m where t is in seconds and the coefficients have the proper units for r to be in metres.
(a)
Find the v and a of the particle?
Answer
v = 3.0î - 4.0t ĵ m/s, a = -4.0ĵ m/s²
(b)
What is the magnitude and direction of velocity of the particle at t = 2.0 s?
Answer
Magnitude = 8.54 m/s, Direction = 69.4° below positive x-axis (or θ = -69.4°)
Explanation
This question is similar to Example 3.4 in the textbook. The velocity is found by differentiating the position vector with respect to time, and acceleration is found by differentiating velocity. The magnitude uses the Pythagorean theorem for vector components, and direction is found using the arctangent of the ratio of y-component to x-component of velocity.