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[多选题]物体做匀加速直线运动，加速度为2m/s2，就是说（　　） A．经过2s的时间，物体速度的变化量是4m/s； B．任意一秒内末速度是初速度的2倍； ...

Mar 19, 2024

[多选题]物体做匀加速直线运动，加速度为2m/s2，就是说（　　） A．经过2s的时间，物体速度的变化量是4m/s； B．任意一秒内末速度是初速度的2倍； C．在任意一秒钟内，物体的初速度可能比末速度大2m/s； D．开始运动一秒后任意时刻的瞬时速度比一秒前的瞬时速度增加2m/s。

Solution

Analyze choice A: Use the equation of motion

v_f = v_i + at

to calculate the change in velocity after 2 seconds. If the initial velocity

v_i

is unknown, we can't confirm the change is exactly 4 m/s without additional information

Analyze choice B: The statement is incorrect because the final velocity after any given second is not necessarily twice the initial velocity; it depends on the initial velocity and the time elapsed

Analyze choice C: This statement could be true if the initial velocity is greater than the final velocity by 2 m/s, but it is not a direct consequence of the acceleration being 2 m/s²

Analyze choice D: Since the acceleration is constant at 2 m/s², the change in velocity every second is 2 m/s. This means that at any time after the motion has started, the instantaneous velocity at time

t

is 2 m/s greater than at time

t-1

. This statement is correct

Key Concept

Equations of Motion (Constant Acceleration): The equation

v_f = v_i + at

relates the final velocity

v_f

to the initial velocity

v_i

, acceleration

a

, and time

t

. For constant acceleration, the change in velocity is directly proportional to time.

Explanation

Choice D is correct because it accurately describes the effect of a constant acceleration on the velocity of an object. With an acceleration of 2 m/s², the velocity increases by 2 m/s every second, regardless of the initial velocity.