Question 1
(a) Find the initial displacement.
\( x=0 \)
(b) Find the displacement at \( t=4\).
\( x=3 \)
(c) Find the velocity during \( 0 \le t \le 3 \).
\( \displaystyle \text{velocity} = \frac{\text{rise}}{\text{run}} = \frac{3-0}{3-0} = 1 \text{ ms}^{-1} \)
(d) Find the velocity during \( 3 \le t \le 7 \).
\( \displaystyle \text{velocity} = \frac{\text{rise}}{\text{run}} = \frac{3-3}{7-3} = \frac{0}{4} = 0 \text{ ms}^{-1} \)
(e) Find the velocity during \( 7 \le t \le 10 \).
\( \displaystyle \text{velocity} = \frac{\text{rise}}{\text{run}} = \frac{0-3}{10-7} = -1 \text{ ms}^{-1} \)
(f) Find the distance travelled for \( 0 \le t \le 10 \).
\( 3+0+3=6 \text{ m} \)
Question 2
(a) Find the initial displacement.
\( x=3 \)
(b) Find the displacement at \( t=4 \).
\( x=-1 \)
(c) Find the velocity during \( 0 \le t \le 5 \).
\( \displaystyle \text{velocity} = \frac{\text{rise}}{\text{run}} = \frac{-2-3}{5-0} = -1 \text{ ms}^{-1} \)
(d) Find the time(s) when the velocity becomes zero.
\( 5 \le t \le 8 \)
(e) Find the time(s) when the velocity becomes positive.
\( 8 \le t \le 10 \)
(f) Find the time(s) when the particle returns to the origin.
\( t=3 \text{ and } 10 \text{ seconds} \)
(g) Find the time(s) when the particle moves backward.
\( 8 \le t \le 10 \)
(h) Find the distance travelled for \( 0 \le t \le 10 \).
\( 5+0+2=7 \text{ m} \)
Question 3
(a) Find the time(s) when the particle changes its direction.
\( t=2 \text{ and } 6 \text{ seconds} \)
(b) Find the distance travelled for the first \( 10 \) seconds.
\( 3+6+3=12 \text{ m} \)
(c) Find the velocity during \( 0 \le t \le 3 \).
\( \displaystyle \text{velocity} = \frac{\text{rise}}{\text{run}} = \frac{3-0}{3-0} = 1 \text{ ms}^{-1} \)
(d) Find the velocity during \( 3 \le t \le 6 \).
\( \displaystyle \text{velocity} = \frac{\text{rise}}{\text{run}} = \frac{-3-3}{6-3} = -2 \text{ ms}^{-1} \)
(e) Find the velocity during \( 6 \le t \le 10 \).
\( \displaystyle \text{velocity} = \frac{\text{rise}}{\text{run}} = \frac{3}{4} \text{ ms}^{-1} \)
(f) Find the maximum speed of the particle.
Speed is the positive value of velocity, thus \( 2 \text{ ms}^{-1} \).
Question 4
(a) Find the time(s) when the particle changes its direction.
\( t=2 \text{ and } 6 \text{ seconds} \)
(b) Find the distance travelled for the first \( 10 \) seconds.
\( 4+8+4=16 \text{ m} \)
(c) Find the time(s) when the particle’s velocity becomes maximum.
velocity is the gradient of \( x \) maximum gradient occurs at \( t=4 \).
(d) Find the time(s) when the particle moves forward.
\( 2 \lt y \lt 6 \)
Question 5
(a) Find the speed when the particle reaches the origin.
\( 1 \text{ms}^{-1} \)
(b) Find the distance travelled for the first \( 10 \) seconds.
\( 10 \text{ m} \)
Question 6
(a) Find the time(s) when the particle changes its direction.
\( t=2 \text{ and } 8 \text{ seconds} \)
(b) Find the time(s) when the particle reaches its maximum velocity.
\( t=0 \text{ and } 10 \text{ seconds} \)
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