A racing car starts from rest at and reaches a final speed at time t . If the acceleration of the car is constant during this time, which of the following statements are true?
(a) The car travels a distance .
(b) The average speed of the car is .
(c) The magnitude of the acceleration of the car is .
(d) The velocity of the car remains constant.
(e) None of statements (a) through (d) is true.
Hence, options (b) and (c) are correct.
The acceleration of the car in the initial state is, ,
Final speed of the car
The expression used to calculate the acceleration of the car is given below.
Put the given value in the expression is:
So, option (C) is correct.
The displacement of the car to use the following kinetic equation will be
The above equation will be rearranged for x ,that is
The average speed of the car is:
So, option (b) is correct.
Two thin rods are fastened to the inside of a circular ring as shown in Figure P2.84. One rod of length D is vertical, and the other of length L makes an angle with the horizontal. The two rods and the ring lie in a vertical plane. Two small beads are free to slide without friction along the rods. (a) If the two beads are released from rest simultaneously from the positions shown, use your intuition and guess which bead reaches the bottom first. (b) Find an expression for the time interval required for the red bead to fall from point A to point C in terms of g and D. (c) Find an expression for the time interval required for the blue bead to slide from point B to point C in terms of g, L, and . (d) Show that the two time intervals found in parts (b) and (c) are equal. What is the angle between the chords of the circle A B and B C? (e) Do these results surprise you? Was your intuitive guess in part (a) correct?
A certain automobile manufacturer claims that its deluxe sports car will accelerate from rest to a speed of 42.0 m/s in 8.00s.
(a) Determine the average acceleration of the car.
(b) Assume that the car moves with constant acceleration. Find the distance the car travels in the first 8.00s.
(c) What is the speed of the car 10.00s after it begins its motion if it can continue to move with the same acceleration?
In a women’s 100-m race, accelerating uniformly, Laura takes 2.00 s and Healan 3.00 s to attain their maximum speeds, which they each maintain for the rest of the race. They cross the finish line simultaneously, both setting a world record of 10.4 s. (a) What is the acceleration of each sprinter? (b) What are their respective maximum speeds? (c) Which sprinter is ahead at the 6.00-s mark, and by how much? (d) What is the maximum distance by which Healan is behind Laura, and at what time does that occur?
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