A motorcycle with an initial velocity of 7.99x10^0 m/s accelerates for a total of 3.3x10^0 seconds at a rate of 1.51x10^0 m/s2. What is it's velocity, to two significant figures?
can anyone show the calculations for this
In 1998, NASA launched DS-1 (Deep Space 1). This spacecraft successfully flew by the asteroid 1992 KD. The propulsion system worked by ejecting argon ions at high speed. The propulsion system could increase the velocity by 7.2284x10^0 m/s per day. What was the average acceleration in m/s2, expressed to 4 significant figures?
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To calculate the final velocity of the motorcycle, we can use the formula:
Final Velocity = Initial Velocity + (Acceleration * Time)
Given:
Initial Velocity (u) = 7.99x10^0 m/s
Acceleration (a) = 1.51x10^0 m/s^2
Time (t) = 3.3x10^0 seconds
Let's substitute the given values into the formula:
Final Velocity = 7.99x10^0 m/s + (1.51x10^0 m/s^2 * 3.3x10^0 seconds)
Now, let's evaluate the product of acceleration and time:
Final Velocity = 7.99x10^0 m/s + (4.983x10^0 m/s)
Now, let's add the values:
Final Velocity = 1.08x10^1 m/s
Rounded to two significant figures, the final velocity of the motorcycle is 11 m/s.
Sure! To solve this problem, we can use the formula of motion:
v = u + at
where:
- v is the final velocity
- u is the initial velocity
- a is the acceleration
- t is the time
Given:
- u = 7.99x10^0 m/s (initial velocity)
- a = 1.51x10^0 m/s^2 (acceleration)
- t = 3.3x10^0 s (time)
Now, let's substitute the given values into the formula and solve for v.
v = u + at
v = 7.99x10^0 m/s + (1.51x10^0 m/s^2)(3.3x10^0 s)
To multiply the numbers in scientific notation, you need to multiply the coefficients and add the exponents:
v = 7.99 x 10^0 m/s + (1.51 x 3.3) x (10^0 m/s^2 x 10^0 s)
v = 7.99 x 10^0 m/s + 4.983 x 10^0 m/s
Now, to add the two values together, ensure the exponents are the same:
v = (7.99 + 4.983) x 10^0 m/s
v = 12.973 x 10^0 m/s
Since we need to round our answer to two significant figures, we consider the first two digits after the decimal point:
v = 13 x 10^0 m/s (as 12.973 rounds up to 13)
Finally, we can rewrite the velocity in standard notation:
v = 13 m/s (to two significant figures)
Therefore, the velocity of the motorcycle, to two significant figures, is 13 m/s.