(Solved):   1,2,3,4,5 1. When any object is in motion, three related characteristics of the motion can ...

 

1,2,3,4,5

1. When any object is in motion, three related characteristics of the motion can be measured. Copy and complete the table. Indicate the appropriate units. (3 marks) 2. For each function, find an expression for the velocity and the value of the displacement and velocity at \( t=5 \). Displacement is in metres and time is in seconds. Include appropriate units in your responses. (4 marks) a. \( s(t)=3 t+7 \) b. \( s(t)=t^{3}-2 t^{2}+4 t-1 \) 3. When a flare is launched from a hilltop, its height above the ground, in metres, at \( t \) seconds is described by \( h(t)=-4.9 t^{2}+16 t+200 \). (5 marks) a. What is the initial velocity of the flare? b. What is the height at launch? c. How fast is the flare descending at \( 6 \mathrm{~s} \) after launch? d. When does the flare hit the ground? e. What is its velocity when it hits the ground? 4. A model rocket is launched with an initial velocity of \( 55 \mathrm{~m} / \mathrm{s} \). Its height as a function of time can be modelled by \( h(t)=-4.9 t^{2}+55 t \). Determine the maximum height reached by the rocket. ( 5 marks) 5. A particle moves along a line. The particle's position, \( s \), in metres at \( t \) seconds is modelled by \( s(t)=2 t^{3}-15 t^{2}+36 t+40 \), where \( t \geq 0 \). (10 marks) a. Determine the initial position of the particle. b. What is the velocity at \( 1 \mathrm{~s} \) and \( 5 \mathrm{~s} \) ? c. When is the particle stationary? d. When is it advancing? Retreating? e. Determine the total distance travelled during the first five seconds. 6. A particle moves along a line. The particle's position, \( s \), in centimetres at \( t \) seconds is modelled by \( s(t)=t^{3}-9 t^{2}+24 t+20 \), where \( t \geq 0 \). What is the total distance travelled by the particle in the first 8 seconds? (5 marks)