University Physics Al No. 1 Rectilinear motion Class Number ame I. Choose the correct answer An object is moving along the x axis with position as a function of time given by x=x(o). Point O is at x=0. The object is definitely moving toward O when (C) (A) 0.(B) <0.(C) d(x) Solution: If the object is moving toward O, the velocity and the position vector of the object have different direction That is xv=x-<0. so the answer is c 2. An object starts from rest at x0 when f0. The object moves in the x direction with positive velocity after f0. The instantaneous velocity and average velocity are related by a)dx/dt <x/ ( B)dx/dt=x/ (c)dx/dt>x/t (D)dx/dt can be larger than, smaller than, or equal to x/t Solution: The instantaneous velocity and average velocity are both positive, the magnitude of them can not be compared 3. An object is moving in the x direction with velocity v(0, and- is nonzero constant. With v.=0 when t=0, then for t>0 the quantity v dv /dt is C (A)Negative. (B)Zero. (C)Positive.(D)Not determined from the information given Solution: As v,=0 when t=0, then for t>0 the velocity v,(t) has the same direction with So we have vx E>0 the answer is C I. Filling the blanks 1. The magnitude of the acceleration of a sports car that can drag race from rest to 100 km/h in 5.00s is 50/9m/s or 5. 56m/s2 Assume the acceleration is constant, although typically this is not a good assumption for automobiles. The ratio of the magnitude of this acceleration to the magnitude of the local acceleration due to gravity (g=9.81 m/s")is_0.57 Solution: According to the definition of the accelerationUniversity Physics AI No. 1 Rectilinear Motion Class Number Name I．Choose the Correct Answer 1. An object is moving along the x axis with position as a function of time given by x = x(t). Point O is at x = 0 . The object is definitely moving toward O when ( C ) (A) 0 d d < t x . (B) 0 d d > t x . (C) 0 d d( ) 2 < t x . (C) 0 d d( ) 2 > t x . Solution: If the object is moving toward O, the velocity and the position vector of the object have different direction. That is 0 d d = ⋅ < t x xv x , so the answer is C. 2．An object starts from rest at x=0 when t=0. The object moves in the x direction with positive velocity after t=0. The instantaneous velocity and average velocity are related by ( D ) (A) dx / dt < x /t . (B) dx / dt = x /t . (C) dx / dt > x /t . (D) dx / dt can be larger than , smaller than, or equal to x/t. Solution: The instantaneous velocity and average velocity are both positive , the magnitude of them can not be compared. 3. An object is moving in the x direction with velocity v (t) x , and t vx d d is nonzero constant. With vx = 0 when t = 0 , then for t > 0 the quantity v v t xd x / d is ( C ) (A) Negative. (B) Zero. (C) Positive. (D) Not determined from the information given. Solution: As vx = 0 when t = 0 , then for t > 0 the velocity v (t) x has the same direction with t vx d d . So we have 0 d d > t v v x x , the answer is C. II. Filling the Blanks 1. The magnitude of the acceleration of a sports car that can drag race from rest to 100 km/h in 5.00s is 50/9m/s2 or 5.56m/s2 . Assume the acceleration is constant, although typically this is not a good assumption for automobiles. The ratio of the magnitude of this acceleration to the magnitude of the local acceleration due to gravity (g = 9.81 m/s2 ) is 0.57 . Solution: According to the definition of the acceleration